Indecomposable Representations of the Nonlinear Angular Momentum Algebra of Quadratic Type^*

The explicit expression for indecomposable representation of the nonlinear angular momentum algebra of quadratic type, $J_2$, on the space of its universal enveloping algebra is given. Then, from this indecomposable representation, other indecomposable (irreducible) representations are derived which are induced on quotient spaces or subduced on invariant subspaces. The inhomogeneous boson and differential realizations of $J_2$ are obtained from the Fock representations corresponding to the indecomposable representations.